Question: What's the first wrong statement in the proof below that $ \triangle BCE \cong \triangle FCE$ $ \; ?$ $ \overline{BC} $ is parallel to $ \overline{DF} $. This diagram is not drawn to scale. $A$ $B$ $C$ $D$ $E$ $F$ Givens $ \overline{BD} \cong \overline{CF}$ $, \ $ $ \angle BDE \cong \angle ECF$ $, \ $ $ \overline{DE} \cong \overline{CE}$ $, \ $ $ \angle ACB \cong \angle ECF$ $, \ $ $ \overline{AC} \cong \overline{CE}$ $, \ $ and $\ $ $ \angle BAC \cong \angle CEF$ Proof $ \triangle FCE \cong \triangle BCA$ because ASA $ \overline{CF} \cong \overline{BC}$ because corresponding parts of congruent triangles are congruent $ \triangle FCE \cong \triangle BDE$ because SAS $ \overline{EF} \cong \overline{BE}$ because corresponding parts of congruent triangles are congruent $ \triangle FCE \cong \triangle BCE$ because SSS
Explanation: Try going through the proof yourself: write down the givens, and then see if they justify the next step for the reason given. Then do the same thing for the next step, and the next, until you run into something that you can't justify, or you finish the proof. There is no wrong statement in this proof.